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29 Cards in this Set
- Front
- Back
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the two important trig sum formulas
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Sin^2x + cos^x2=1
1+tan^2x=Sec^2x |
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DISK method
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v= pie integral rX^2 dx
(representative shells perpendicular- dx matches direction of rotation) |
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WASHER method
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v= pie integral Rx^2 - rx^2 dx
(representative shells perpendicular- dx matches direction of rotation) |
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SHELL method
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v= 2pie integral px * hx dx
(representative shells parallel to direction of rotation - dy for horizontal(x) rotation). |
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arc length
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formula given, pay attention to bounds
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Work =
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w=fd
integral Fx dx or integral Dx df |
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INTEGRATION BY PARTS FORMULA!!!!!!!!!!!!!!!
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integral u dv = uv - integral v du
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Tabular:
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alternate signs
u column (derivative) dv column (integrate) cross multiply |
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integrating sin and cos when one power of either is odd
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save one factor and convert the remaining to opposites. expand. integrate.
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integrating sin and cos when both powers are even
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use half angle identity formulas (given on formula sheet) .
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how to integrate sec and tan if either has an odd power
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save on factor, convert the remaining, expand, integrate.
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how to integrate- when there are NO sec factors, and tan is odd and positive
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convert tan to sec^2 , expand, integrate.
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how to integrate when there are No tan factors and sec is off
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use integration by parts
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last resort with sec/tan integration problems
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try converting to cos&sin
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when is the partial fraction method not necessary-
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when deriv of botton is on the top- then use the log rule. (potential u sub).
when polynomial can be simplified to the point where we can use the log rule. (potential u sub) -be sure that the degree on the bottom is LARGER than the degree on the top. |
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d/dx sinu
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cosu * u'
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d/dx cos u
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-sinu*u'
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d/dx tan u
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sec^2u * u'
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d/dx cot u
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-csc^2 u * u'
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d/dx csc u
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(-csc u cot u) u'
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integral cos
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sin
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integral sin
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-cos
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integral tan
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-ln (cos u)
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integral cot
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ln(sin u)
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integral sec^2
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tan u
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integral csc^2
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-cot u
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csc x
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1/sinx
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secx
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1/cosx
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cotx
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1/tanx
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